1. What are the four types of relationships that children should develop with numbers 1 through 10? Give an example of each type of relationship. (Chapter 8)
Patterned sets: Recognizing groups of objects as patterns. Example-Using paper plates and peel-off dots, create patterns of numbers and use them as flashcards to help students identify patterns.
One and two more, one and two less: Understanding the relationships between numbers; like 2 is one more than 1 and 2 less than 4. Example-Using a plastic cup, counters, flashcards with a number on them and flashcards that say 1 more/less, 2 more/less. One student chooses a card with a number and they place that amount of counters i the cup. Then, another student picks a card that either says more or less and they put or take out more counters.
Anchors or "benchmarks" of 5 and 10: Finding the relationships of numbers 1 through 10. Example-Using frames of 5 or 10 and using counters, give students a number and let them show it whatever way they want. Discuss the numbers needed to make 5 or 10.
Part-part-whole relationships: Viewing a number as made up of two sets of numbers. Example-Make a list of 3 numbers (7-5-2) for one number (9). Tell the students that 2 of the 3 numbers make up the number (7-2).
2. What are the benefits of developing a "think-addition" approach for subtraction? How does it compare to a "count what's left" approach? (Chapter 9)
A benefit of developing a "think-addition" approach is that the student uses prior knowledge of addition facts to solve subtraction problems. Another benefit is that it helps to make the problem easier to solve because most of the time, students feel that they need to work backwards and using this approach encourages them to be able to solve them. Especially with numbers that are greater than 10, students feel more comfortable counting towards the biggest number. For example, 16-8, it is quicker to count up to 16 (8 and what makes 16?). Rather than counting back from 16. The "count what's left" approach is exactly that! The students end up counting and counting more than the "think-addition" approach. They will have to count 16, then count off 8 and finally, count off what is left in order to find the answer. In comparison, the "count what's left" approach is definitely much more hard for the students to comprehend.
Review Questions #1
1. What are the four types of relationships that children should develop with numbers 1 through 10? Give an example of each type of relationship. (Chapter 8)
Patterned sets: Recognizing groups of objects as patterns. Example-Using paper plates and peel-off dots, create patterns of numbers and use them as flashcards to help students identify patterns.
One and two more, one and two less: Understanding the relationships between numbers; like 2 is one more than 1 and 2 less than 4. Example-Using a plastic cup, counters, flashcards with a number on them and flashcards that say 1 more/less, 2 more/less. One student chooses a card with a number and they place that amount of counters i the cup. Then, another student picks a card that either says more or less and they put or take out more counters.
Anchors or "benchmarks" of 5 and 10: Finding the relationships of numbers 1 through 10. Example-Using frames of 5 or 10 and using counters, give students a number and let them show it whatever way they want. Discuss the numbers needed to make 5 or 10.
Part-part-whole relationships: Viewing a number as made up of two sets of numbers. Example-Make a list of 3 numbers (7-5-2) for one number (9). Tell the students that 2 of the 3 numbers make up the number (7-2).
2. What are the benefits of developing a "think-addition" approach for subtraction? How does it compare to a "count what's left" approach? (Chapter 9)
A benefit of developing a "think-addition" approach is that the student uses prior knowledge of addition facts to solve subtraction problems. Another benefit is that it helps to make the problem easier to solve because most of the time, students feel that they need to work backwards and using this approach encourages them to be able to solve them. Especially with numbers that are greater than 10, students feel more comfortable counting towards the biggest number. For example, 16-8, it is quicker to count up to 16 (8 and what makes 16?). Rather than counting back from 16. The "count what's left" approach is exactly that! The students end up counting and counting more than the "think-addition" approach. They will have to count 16, then count off 8 and finally, count off what is left in order to find the answer. In comparison, the "count what's left" approach is definitely much more hard for the students to comprehend.